A. Direct Modulation vs. External Modulation of Semiconductor Laser Output
The continuing increase of transmission rates at all levels of telecommunication networks and fiber-based RF photonic systems raises demand for very high-speed, low-cost optical transmitters. Much effort has been put into developing wide-bandwidth lasers and modulators over the past ten years. To date, the largest reported bandwidth of directly modulated free-running semiconductor lasers at 1.55 μm is 30 GHz, as measured in a Fabry-Perot edge-emitting buried-heterostructure multiple-quantum-well (MQW) laser [Matsui 1997 reference] and in a DFB laser [Kjebon 1997 reference]. On the other hand, external modulators operating at speeds of 40 Gb/s are currently available commercially [Covega 2012 reference] and modulators operating at speeds in the 100-GHz range are under development [Chang 2002 reference]. The widest reported 3-dB modulation bandwidth for Ti:LiNbO3 electro-optic (EO) modulators is 70 GHz, with the maximum measured frequency of 110 GHz [Noguchi 1998 reference]. The drawback of the Ti:LiNbO3 modulators, however, is their poor sensitivity, as represented by their unattractively high half-wave voltage Vπ. Very high modulation frequency and broadband performance of the Ti:LiNbO3 modulators come at the expense of too high Vπ (exceeding 10 V, while the desirable voltage is below 1V), which makes them less attractive for system applications [Cox 2006 reference]. A very impressive 145 GHz modulation bandwidth has been demonstrated for a polymer EO modulator at 1310 nm [Lee 2002 reference]. However, the technology of polymer modulators is still very immature, with most of the development effort being focused on the polymer material itself. In general, polymers with larger EO effect are the least stable against temperature and optical power, which casts doubt on long-term stability of polymer materials [Cox 2006 reference]. In addition, the frequency response of any EO modulator is typically determined by the electrode RF propagation loss and the phase mismatch between the optical beam and modulation microwave [Chung 1991 reference], [Gopalakrishnan 1994], [Chang 2002 reference], which makes overall design and fabrication of these devices complex and costly. Therefore, low-cost small-size directly modulated laser sources with very high modulation bandwidths exceeding 100 GHz are still highly desirable for the rapidly growing applications of RF optical fiber links, and could revolutionize the future of optical telecommunication.
B. Enhancement of Modulation Bandwidth in Injection-Locked Semiconductor Lasers
Since their inception, semiconductor lasers have been key components for many applications in optical fiber communication because of their excellent spectral and beam properties and capability to be directly modulated at very high rates. However, their frequency response has limited the commercial use of directly modulated lasers to digital transmission not exceeding 10 Gb/s. The modulation response of a diode laser is determined by the rate at which the electrons and holes recombine in the active region (spontaneous carrier lifetime τc), and the rate at which photons can escape from the laser cavity (photon lifetime τp). The modulation bandwidth is limited by the relaxation-oscillation frequency fRO of the laser given by [Lau 1985]2πfRO=√{square root over (gNγpP0)},  (1)where gN is the differential optical gain, P0 is the average photon number in the laser cavity, and γP is the photon decay rate given by the reciprocal of τp. Eq. (1) suggests that the relaxation-oscillation frequency can be increased by proper design of laser parameters to get either higher photon density or shorter photon lifetime. Increased injection currents for higher P0 values and shorter laser cavities for smaller τp are ordinarily employed for that purpose in diode lasers. Both approaches, however, involve higher injection current densities, which could result in optical damage to the laser facets and excessive heating. Safe levels of injection current therefore limit the modulation bandwidth in semiconductor lasers.
Optical injection locking has been actively researched for its potential to improve ultrahigh-frequency performance of semiconductor lasers and to reach beyond the record values of modulation bandwidth achieved for free-running devices [Lau 2009 reference]. Injection locking was first demonstrated in 1976 using edge-emitting lasers [Kobayashi 1976 reference], and in 1996 for vertical-cavity surface-emitting lasers (VCSELs) [Li 1996 reference]. The technique uses output of one laser (master) to optically lock another laser (slave), which can still be directly modulated. Significant increase in the resonance frequency and modulation bandwidth, accompanied by reduction in nonlinear distortions [Meng 1999 reference] and frequency chirp [Mohrdiek 1994 reference], has been achieved by injecting external light into diode lasers. So far, improved microwave performance has been observed in edge-emitting lasers with Fabry-Perot cavity; see references [Simpson 1995], [Simpson 1997], [Jin 2006], DFB lasers [Meng 1998], [Hwang 2004], [Sung 2004], [Lau 2008b], and VCSELs [Chrostowski 2002], [Chrostowski 2003], [Okajima 2003], [Chang 2003], [Zhao 2004], [Zhao 2006], [Chrostowski 2006a], [Chrostowski 2006b], [Wong 2006], [Lau 2008b]. The highest experimentally observed 3-dB modulation bandwidth of ˜80 GHz, by far exceeding those achieved for free-running devices, has been reported in injection-locked VCSELs and DFB lasers [Lau 2008b].
Many aspects of the injection-locking experimental results have been reproduced in analytical studies; references [Luo 1991], [Simpson 1996], [Nizette 2001, [Nizette 2002], [Lau 2007], [Lau 2008a] and numerical simulations using rate equation models [Luo 1990], [Luo 1992a, [Luo 1992b], [Liu 1997], [Jones 2000], [Chen 2000], [Murakami 2003], [Wieczorek 2006]. Dynamic behavior of diode lasers is described by a system of coupled nonlinear differential equations for the optical field and carrier density in the laser cavity. While for a free-running laser these equations exhibit only damped oscillations with corresponding relaxation-oscillation frequency and damping rate, external optical injection increases the number of degrees of freedom by one, which leads to a much greater variety of dynamic behavior. In particular, perturbation analysis of rate equations, references [Simpson 1996, [Simpson 1997], revealed that the enhanced resonance frequency (the peak frequency in the modulation-frequency response) was identical to the difference between the injected light frequency and a shifted cavity resonance, which agreed well with experimental observations, the physical mechanism of the effect being clarified by references [Murakami 2003], [Wieczorek 2006]. Under strong optical injection, a beating between the injected light frequency and the cavity resonant frequency dominates the dynamic behavior.
C. Limitations of Injection-Locked Edge-Emitting Lasers and VCSELs
Since the detuning between frequencies of the injected light and the cavity mode controls the enhanced resonance frequency in the modulation response of injection-locked semiconductor lasers, obtaining the widest possible stable locking range in terms of the frequency detuning becomes the immediate goal. Strong optical injection is therefore crucial for reaching the ultimate limits of modulation bandwidth enhancement in injection-locked lasers. The coupling rate coefficient κc for optical injection locking is:κc=c√{square root over (1−R)}/(2neffL)=√{square root over (1−R)}/τrt,  (2)where R is the reflectivity of the laser mirror through which the light is injected, L is the cavity length, c is the speed of light, neff is the effective index, and τrt=2neff L/c is the cavity roundtrip time.
The smallest possible values for both cavity roundtrip time τrt and reflectivity R of the mirror used for injection (maximizing the injection coupling rate coefficient κc) would be ideal for that application. However, as dictated by the requirement to keep threshold current at an acceptable level, the inherent design trade-off between these parameters makes further optimization of both edge-emitting lasers and VCSELs for enhanced high-speed performance very problematic. In edge-emitting lasers, the beneficial effect of rather low mirror reflectivity R on the injection coupling rate coefficient κc is counteracted by large τrt resulting from long laser cavities. Similarly, even though injection-locked VCSELs benefit greatly from very short cavities and, hence, very small τrt, their high-speed performance, at the same time, is compromised by very high mirror reflectivity of a typical VCSEL, resulting in coupling rate coefficients similar to edge emitters. Further enhancement of resonance frequency in injection-locked edge-emitting lasers and VCSELs is expected to come solely from higher power master lasers used for optical injection. For this reason, more complicated cascaded schemes have been attempted, with demonstrated improvement in modulation bandwidth as compared to solitary injection-locked VCSELs [Zhao 2007 reference]. The cascaded optical injection locking is a very promising technique that has scaling-up potential to eventually reach very wide modulation bandwidth over 100 GHz by cascading more slave lasers in a daisy chain structure, as long as the master laser has enough power to stably lock the slave laser with the largest detuning value [Zhao 2007]. This, however, can hardly be realized with VCSELs, notable for their very high mirror reflectivity. In addition, VCSELs pose a very challenging alignment problem in injection-locking experiments and, at the same time, are not suitable for monolithic integration when injection locking is the requirement. The inventors believe VCSELs are very hard to be optimized for any further improvement in their speed.
D. Strongly Injection-Locked Whistle-Geometry Microring Lasers
To overcome the limitations of injection-locked edge-emitting lasers and VCSELs described above, a novel injection locking scheme (FIG. 1), involving a DBR master laser monolithically integrated with a unidirectional whistle-geometry microring laser (WRL), was developed and is described in U.S. Pat. No. 8,009,712, the teachings of which are incorporated herein by reference. The DBR/WRL geometry allows for strong coupling of the master laser output into the ring slave laser, providing dramatically increased injection coupling rate. By the very nature of WRL, low reflectivity for incident light would not at all compromise the quality of the ring cavity, and would not affect the threshold condition for the wave propagating in the favored direction. This makes WRLs free from the design constraints that edge-emitting lasers and VCSELs suffer from.
The advantage of the novel injection-locking scheme was confirmed in numerical modeling; references [Smolyakov 2011a], [Smolyakov 2011b]. The dynamics of an optically injection-locked WRL monolithically integrated with single-mode master DBR laser was modeled by a system of rate equations written in terms of the photon numbers, phases, and total carrier numbers in the master DBR and microring slave lasers.
The master laser was modeled as a single-mode laser described by the photon number Sm and the optical phase θm, related to the master laser field Em as Em=√{square root over (Sm)}expiθm(t):
                                                        ⅆ                              S                m                                                    ⅆ              t                                =                                                    [                                                                            G                                              0                        ⁢                                                                                                  ⁢                        m                                                              ⁡                                          (                                                                        N                          m                                                -                                                  N                                                      0                            ⁢                                                                                                                  ⁢                            m                                                                                              )                                                        -                                      1                                          τ                      p                      m                                                                      ]                            ⁢                              S                m                                      +                          R              sp                                      ,                            (        3        )                                                      ⅆ                          θ              m                                            ⅆ            t                          =                                            α              2                        ⁡                          [                                                                    G                                          0                      ⁢                                                                                          ⁢                      m                                                        ⁡                                      (                                                                  N                        m                                            -                                              N                                                  0                          ⁢                                                                                                          ⁢                          m                                                                                      )                                                  -                                  1                                      τ                    p                    m                                                              ]                                .                                    (        4        )            A uniform carrier density was assumed in the laser cavity, with the following rate equation describing time evolution of the total carrier number Nm in the master DBR laser:
                                          ⅆ                          N              m                                            ⅆ            t                          =                                            η              i                        ⁢                                          I                m                            q                                -                                    N              m                                      τ              c                                -                                                    G                                  0                  ⁢                                                                          ⁢                  m                                            ⁡                              (                                                      N                    m                                    -                                      N                                          0                      ⁢                                                                                          ⁢                      m                                                                      )                                      ⁢                                          S                m                            .                                                          (        5        )            In Eqs. (3)-(5), G0m is the differential modal gain, given by
                                          G                          0              ⁢                                                          ⁢              m                                =                                    Γ              ⁢                                                          ⁢                              av                g                                                    V              m                                      ,                            (        6        )            where Γ is the optical confinement factor, α is the differential gain, vg is the group velocity, and Vm is the master laser active region volume. Other parameters in Eqs. (3)-(5) are the linewidth broadening factor α, the transparency carrier number N0m, the carrier lifetime τc, the photon lifetime τpm, the spontaneous emission rate Rsp, and the internal quantum efficiency ηi.
The ring laser was modeled by two counterpropagating modes with photon numbers Scw, Sccw and optical phases θcw, θccw for the clockwise (CW) and counterclockwise (CCW) modes, respectively. The master laser light was assumed to be injected into the CCW mode:
                                                        ⅆ                              S                ccw                                                    ⅆ              t                                =                                                    [                                                      G                    ccw                                    -                                      1                                          τ                      p                      ccw                                                                      ]                            ⁢                              S                ccw                                      +                          R              sp                        +                          2              ⁢                                                          ⁢                              κ                c                            ⁢                                                                    S                    m                                    ⁢                                      S                    ccw                                                              ⁢                              cos                ⁡                                  (                                                            θ                      ccw                                        -                                          θ                      m                                                        )                                                                    ,                            (        7        )                                                                    ⅆ                              θ                ccw                                                    ⅆ              t                                =                                                    α                2                            ⁡                              [                                                      G                    ccw                                    -                                      1                                          τ                      p                      ccw                                                                      ]                                      -                          (                                                ω                  0                                -                                  ω                  th                                            )                        -                                          κ                c                            ⁢                                                                    S                    m                                                        S                    ccw                                                              ⁢              sin              ⁢                                                          ⁢                              (                                                      θ                    ccw                                    -                                      θ                    m                                                  )                                                    ,                            (        8        )                                                          ⁢                                                            ⅆ                                  S                  cw                                                            ⅆ                t                                      =                                                            [                                                            G                      cw                                        -                                          1                                              τ                        p                        cw                                                                              ]                                ⁢                                  S                  cw                                            +                              R                sp                                              ,                                    (        9        )                                                          ⁢                                            ⅆ                              θ                cw                                                    ⅆ              t                                =                                                    α                2                            ⁡                              [                                                      G                    cw                                    -                                      1                                          τ                      p                      cw                                                                      ]                                      -                                          (                                                      ω                    0                                    -                                      ω                    th                                                  )                            .                                                          (        10        )            A uniform carrier density was assumed in the ring laser cavity, with the following rate equation describing time evolution of the carrier number Nr in the ring laser:
                                          ⅆ                          N              r                                            ⅆ            t                          =                                            η              i                        ⁢                                          I                r                            q                                -                                    N              r                                      τ              c                                -                                    G              cw                        ⁢                          S              cw                                -                                    G              ccw                        ⁢                                          S                ccw                            .                                                          (        11        )            
Eqs. (7)-(10) allow for unequal photon lifetimes τpcw and τpccw for the CW and CCW modes, respectively. Nonlinear gain saturation effects were taken into account in Eqs. (7)-(11) by coefficients εs and εc for the self- and cross-gain saturation in the expressions for the modal gain:
                                                        G              cw                        =                                                            G                                      0                    ⁢                                                                                  ⁢                    r                                                  ⁡                                  (                                                            N                      r                                        -                                          N                                              0                        ⁢                                                                                                  ⁢                        r                                                                              )                                                            1                +                                                      ɛ                    s                                    ⁢                                                            S                      cw                                        /                                          V                      r                                                                      +                                                      ɛ                    c                                    ⁢                                                            S                      ccw                                        /                                          V                      r                                                                                                    ;                ⁢                                  ⁢                                            G              ccw                        =                                                            G                                      0                    ⁢                                                                                  ⁢                    r                                                  ⁡                                  (                                                            N                      r                                        -                                          N                                              0                        ⁢                                                                                                  ⁢                        r                                                                              )                                                            1                +                                                      ɛ                    s                                    ⁢                                                            S                      ccw                                        /                                          V                      r                                                                      +                                                      ɛ                    c                                    ⁢                                                            S                      cw                                        /                                          V                      r                                                                                                    ,                                    (        12        )            with N0r standing for the transparency carrier number, and the differential modal gain given by
                                          G                          0              ⁢                                                          ⁢              r                                =                                    Γ              ⁢                                                          ⁢                              av                g                                                    V              r                                      ,                            (        13        )            where Vr is the ring laser active region volume. Other parameters in Eqs. (7)-(11) are the injection coupling rate κc, the mode frequency of the ring cavity ω0, and the free-running mode frequency ωth of the ring cavity at threshold. More details of a 1.55-μm InGaAs/AlGaInAs/InP MQW deeply etched ridge-waveguide laser structure, assumed in the simulation, are given in reference [Smolyakov 2011b].
In calculating the modulation response, a small-signal modulation was applied to the ring laser injection current Ir of Eq. (11) in the formIr=I0r[1+δsin(2πft)],  (14)where I0r is the injection current at a constant ring laser bias, f is the modulation frequency, and δ is the modulation depth. 1% modulation depth (δ=0.01) was assumed throughout the simulations.
Greatly enhanced resonance frequency of up to ˜160 GHz was predicted in numerical calculations for the strongly injection-locked ring laser (FIG. 2). Typical of all optical injection-locking schemes, however, the modulation response showed a very significant reduction in the modulation efficiency between low frequencies and the resonance frequency, which limits the usefulness of the novel scheme to narrow-band applications.
E. Strongly Injection-Locked Cascaded Whistle-Geometry Lasers
One possible way to overcome the low-frequency roll-off problem and to attain tailorable and broad modulation bandwidth is to use cascaded injection locking [Zhao 2007 reference]. With the frequency detuning between the injected light and the cavity resonant frequency corresponding to the enhanced resonance frequency in the modulation response of an injection-locked semiconductor laser, adding more slave lasers to the cascaded injection-locking configuration, all injection-locked by the same master laser but with different detunings, results in multiple resonance peaks in the modulation response of the slave laser of the last stage, provided the first slave laser is directly modulated, whereas all the others are modulated indirectly through the modulated optical output of the previous stage.
Using that concept, the injection-locking scheme of FIG. 1 can be modified to a cascaded system with two strongly injection-locked whistle-geometry unidirectional ring lasers (FIG. 3), where the modulated optical output of the first ring laser is used to injection-lock the second ring laser; references [Smolyakov 2012a], [Smolyakov 2012b], as described in the inventors' U.S. Pat. No. 8,009,712, the teachings of which are incorporated herein by reference. FIG. 4 shows modulation-frequency response of the free-running ring laser and that of the second ring laser in the cascaded injection-locking scheme of FIG. 3, calculated for several positive values of frequency detuning Δω2. For comparison, modulation-frequency response in each case is normalized to the low-frequency response of the free-running laser. One can clearly see further enhancement of the modulation response as the second resonance peak occurring at a lower modulation frequency, corresponding to the frequency detuning Δω2 between the master and the second ring laser.
In order to illustrate further improvement in the modulation response of the cascaded injection-locking scheme of FIG. 3, as compared to that of the injection-locking scheme of FIG. 1, FIG. 5 shows the modulation response calculated for the two injection-locking schemes under identical bias conditions at frequency detunings Δω1=100 GHz and Δω2=50 GHz between the master and the first and the second ring lasers, respectively. The modulation response in both cases is normalized to the low-frequency response of the injection-locking scheme of FIG. 1. Obvious improvement is seen in the modulation response of the cascaded injection-locking scheme, showing a 3-dB modulation bandwidth of ˜117 GHz, as compared to that of ˜17.3 GHz obtained for the injection locking with a single ring laser.
F. Strongly Injection-Locked Microring Lasers with Modulated Photon Lifetime
As discussed in Section E, the dip in frequency response of a single WRL, shown in FIG. 2, is expected to be moderated by utilizing an injection-locking scheme with multiple cascaded ring lasers (cf. FIGS. 4 and 5 that show the expected improvement with just one additional WRL), which should result in a flat, broadband modulation response. Monolithically integrating multiple cascaded ring lasers on a common substrate would, however, complicate the design of the optoelectronic integrated circuit (OEIC), and a solution that would achieve the same goal with a single ring laser is highly desirable. Pursuant to an embodiment of the invention, the inventors provide novel injection-locked WRLs with directly modulated photon lifetime, rather than modulated injection current, as an elegant solution to the task of flattening the frequency response and achieving a broadband transmitter operating at frequencies beyond 100 GHz.
Photon-lifetime (and therefore cavity-Q) modulation as a means of improving the high-frequency response of semiconductor lasers was independently proposed theoretically in references [Avrutin 1993] and [Dods 1994] for the edge-emitting DBR lasers and VCSELs, respectively. Subsequently, the concept has been extended to bidirectional ring lasers coupled to external EO or electroabsorption (EA) modulators in a compound cavity [Dai 2009 reference]. The photon-lifetime modulation mechanism directly affects the photon density in the laser cavity and is potentially much faster than the conventional injection current modulation that affects the photon density indirectly through relatively slowly varying carrier density. The photon lifetime in a laser above threshold is much shorter than the carrier lifetime. In addition, photon-lifetime modulation offers an advantage of reducing the wavelength chirp, which is quite large in directly modulated diode lasers, while maintaining a stable output wavelength [He 2007], [Dai 2009]. The latter feature requires a careful anti-resonant design of Q-modulator in multi-section DFB lasers; see references [He 2007], [Liu 2010], but is readily achievable in the scheme of this invention by virtue of locking to the stabilized master wavelength.
Employing direct cavity-Q modulation, rather than injection-current modulation, as an effective way to eliminate the low-frequency roll-off in modulation response of injection-locked semiconductor lasers has been investigated theoretically in [Wang 2011 reference] using small-signal and numerical analyses. While the enhanced resonant frequency in Q-modulated injection-locked lasers remained the same as in current-modulated lasers, a significant enhancement in 3-dB bandwidth has been demonstrated in numerical analysis due to elimination of low-frequency roll-off. The modulation response of conventional current-modulated lasers is known to decay as 1/ω2 above the resonance frequency. In contrast, the frequency response in Q-modulated lasers decays as 1/ω) at frequencies beyond the resonance frequency, thus allowing a much broader modulation bandwidth, references [Avrutin 1993], [He 2007], [Liu 2010].
Pursuant to an embodiment of the present invention, the inventors have analyzed the potential of cavity-Q-modulation mechanism for the strongly injection-locked WRL of FIG. 1. Modulation was applied to the optical loss term 1/τpccw in Eqs. (7), (8) in the form:1/τpccw=[1+δsin(2πft)]/(τpccw)0,  (15)where f is the modulation frequency and δ is the modulation depth. 1% modulation depth for the optical loss (δ=0.01) was assumed in the simulations. In agreement with earlier analyses, much slower decay of the free-running laser modulation response was obtained for the laser modulated through optical loss (FIG. 6). Complete elimination of the low-frequency roll-off and 3-dB modulation bandwidth up to 200 GHz are predicted in the numerical analysis (FIG. 7) for the modulation scheme combining advantages of Q-modulation and strong optical injection locking of WRL.